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- Volume 39, Issue 4, 1991
Geophysical Prospecting - Volume 39, Issue 4, 1991
Volume 39, Issue 4, 1991
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ANALYSIS OF THE COMMON MIDPOINT GATHER BY DECOMPOSITION INTO ELEMENTARY WAVEFRONTS1
Authors PIERRE THORE and ERIC DE BAZELAIREAbstractThe imaginary wavefront of a common midpoint gather of seismic data is analysed in terms of elementary wavefronts. The wavefronts emitted by the sources are split into a sequence of elementary circular wavefronts. Each such wavefront is independently transmitted through the subsurface and received by a group of receivers associated with the sources. The theory is first demonstrated in the case of a one‐layer medium and is then extended to the case of a multilayer medium.
We show that pairs of imaginary stationary points F and F' occur in the first medium through which all the rays, corresponding to the group of sources and receivers associated with the elementary wavefront pass. The location of the points is determined by 2n equations with 2n unknowns; (2n ‐ 1) of these equations correspond to n layers of the medium, and an additional equation is given by the geometry of the CMP gather. Applying Fermat's principle between the points F and F', we obtain an algorithm for CMP ray tracing. The wavefront sampling problem is considered but not theoretically solved. Results obtained in the general case (a multilayer medium with lateral velocity variation) are presented and compared with those obtained by other modelling techniques.
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PARAXIAL RAY TRACING IN 3D INHOMOGENEOUS, ANISOTROPIC MEDIA1
Authors RICHARD L. GIBSON Jr, ARCANGELO G. SENA and M. NAFI TOKSÖZAbstractMany investigations of the propagation elastic waves within the earth require a technique for producing synthetic seismograms which is capable of modelling 3D propagation effects. Ray methods are an excellent option for these problems, because they can be made fully 3D and allow a relatively quick and flexible computation of synthetic seismograms. However, the two point problem of finding the ray which connects exactly a specific source and receiver, may still be difficult and time consuming. Therefore, application of the paraxial method, which allows extrapolation of the information on a given ray to nearby receiver locations, is very valuable. With this approach, great savings in computation time and significant simplification of computer codes are possible.
We investigate the application of the paraxial ray method to two problems in which the effects of 3D seismic wave propagation are important. The first is a model of a reef structure. In this case, we consider synthetic seismograms for a VSP experimental configuration. When the SV source and well are located along the axis of the reef, only 2D propagation effects are observed. If the source‐receiver plane is located to the side of the reef, however, the 3D shape of the reef causes significant amplitudes to be predicted for shear‐wave arrivals on the transverse component of the synthetic seismograms.
The second example is a ID, layered earth model, but it includes two layers which are azimuthally anisotropic due to the presence of aligned, vertical fractures. This anisotropy leads to 3D raypaths. Synthetic seismographs are presented for a cross‐hole geometry both for an equivalent isotropic model and for the direction parallel to the fractures and at an angle of 45° to the fractures in the anisotropic case. These synthetics show that the differences between the isotropic case and the case for source and receivers aligned with the plane of the fractures are small and subtle. On the other hand, the predictions for the direction at 45° to the cracks show shear‐wave splitting and significant transverse component signal.
These results have important implications for both modelling and for applications such as tomography. It is clear that for some of the cases considered, a 2D algorithm will lead to errors in interpretation of data. In addition, ray‐based tomographic techniques will have great difficulty in obtaining a well‐defined 2D planar image when the signals are propagating in regions outside the image plane.
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LONG‐OFFSET TRANSIENT EM SOUNDING NORTH OF THE RHINE‐RUHR COAL DISTRICT, GERMANY1
Authors A. STEPHAN, H. SCHNIGGENFITTIG and K.‐M. STRACKAbstractDuring the past two decades electromagnetic methods have been increasingly applied to problems in hydrocarbon exploration. It has been shown that EM methods achieve satisfactory results which can be supplementary to results of the seismic method. We extend the application of the Long‐Offset Transient ElectroMagnetic Sounding (lotem) to exploration problems in the coal mining industry.
A survey was conducted north of the Rhine‐Ruhr coal district using a grounded dipole source and receivers laid out along several profile lines giving areal coverage. The strong noise from cultural as well as natural electromagnetic sources was reduced using prestack data processing techniques resulting in reliable data with a good signal‐to‐noise ratio. The interpretation is self‐consistent and matches the well logs and the geological information of the area quite well. The high station density permitted the mapping of the top of the Carboniferous formation to a depth of between 800 and 1000 m below surface.
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A FIRST‐ORDER CORRECTION TO THE THEORY FOR THE ELECTROMAGNETIC RESPONSE OF A THIN CONDUCTING SHEET1
Authors D. G. HURLEY and P. F. SIEWAbstractThe eddy currents induced in a thin conducting sheet by a sinusoidally varying primary magnetic field are investigated in the low‐frequency limit when the depth of penetration of the primary field is much greater than the thickness of the sheet. A perturbation scheme in terms of the small parameter, δ, which is the ratio of the thickness of the sheet to the length scale of the primary field is initiated. The zero‐order terms in δ give the familiar results that were first obtained by Maxwell. The first‐order terms in δ depend on the tangential as well as the normal component of the primary field and give eddy‐current distributions that vary quadratically across the sheet. The boundary conditions that determine the accompanying secondary magnetic field are derived. Detailed results are given when the primary field is that due to a dipole.
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MEASURED REFLECTION STRENGTHS OF UNDERWATER PIPES IRRADIATED BY A PULSED HORIZONTAL DIPOLE IN AIR: COMPARISON WITH CONTINUOUS PLANE‐WAVE SCATTERING THEORY1
Authors W. A. WENSINK, J. HOFMAN and J. K. VAN DEENAbstractAt Delft Geotechnics the technique of ground‐penetrating radar is in use for the detection of buried objects such as pipes. In order to give our ‘measurements in the field’ a more quantitative interpretation, a series of experiments has been started under well‐defined conditions.
A cylindrical vessel contains water, simulating wet soil. A pulsed transmitting antenna (TA) is mounted above the water‐surface irradiating horizontal underwater pipes. The reflected pulses are detected by a horizontal receiving dipole (AP, i.e. ‘air‐probe’) in the air. The reflecting objects used in the experiments are steel pipes, PVC rods and hollow PVC pipes filled with air or water. The depth of the pipes varies from 0.25 to 2 m. The strength of the reflected pulse depends on the type of pipe, its diameter, its depth, the electromagnetic properties of the water and also on the strength and polarization of the incident E‐field. The latter is (mainly) parallel to the axis of the pipe in the present experiments.
The experimental results have been compared with calculated results using the theory of a continuous plane wave, incident on an infinitely long cylinder in a homogeneous dielectric medium with the same dielectric constant as water. In a previous paper an experiment was described in which a movable receiving dipole in the water measured the transverse, mutually orthogonal Eø‐ and Eθ‐components of the pulses emitted by the TA. The amplitudes of Eθ versus depth, measured in that paper, are used in the calculations as amplitudes of the incident field. The attenuation of the scattered field is accounted for by assuming exponential damping. The relative amplitudes of the scattered field for different pipes lying at the same depth are reproduced very well by this simple theory. Also the relative values of the scattered amplitudes for a given pipe lying at different depths are described neatly, provided the refraction of the scattered field at the water‐air interface is accounted for.
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INTERPRETATION OF VLF‐EM IN‐PHASE DATA USING CURRENT DENSITY PSEUDOSECTIONS1
Authors R. D. OGILVY and A. C. LEEAbstractThe interpretation of VLF‐EM surveys in terms of buried conductors can be assisted by the application of a linear filter to the observed in‐phase component of the vertical magnetic field. One such scheme is examined critically by using the calculated response from a variety of synthetic models to compute theoretical current density pseudosections.
The results confirm that this filter technique provides a useful complementary tool for studying the third (i.e. depth) dimension. For single, steeply dipping plates (> 45°) diagnostic information may be derived concerning the depth, size, lateral location, and direction of dip, since the current density maxima seems always to occur within the conductor or at least within one data interval.
However, there are some limitations which do not appear to be widely recognized. For single plates the angle of dip cannot be resolved by the current density transformation. Pattern distortions can occur where targets are in close proximity, where the cross‐sectional form of the conductor is complex or where the dip is shallow (< 45°). In these latter cases the current density maxima may not occur within the conductive structure and therefore cannot be used to infer depth of burial and/or conductor shape with the same degree of confidence.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)